An uncountable countable set
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From: Virgil on 25 Oct 2006 16:09 In article <453fb621(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > Tony Orlow wrote: > >> Virgil wrote: > >> < endless reiterations of the following > > >>> The only question is "According to the rules set up in the problem, is > >>> each ball which is inserted into the vase before noon also removed from > >>> the vase before noon?" > >>> > >>> An affirmative answer confirms that the vase is empty at noon. > >>> A negative answer violates the conditions of the problem. > >>> > >>> Which answer does TO choose? > >> God, are you a broken record, or what? Let's take this very slowly. Ready? > >> > >> Each ball inserted before noon is removed before noon, but at each time > >> before noon when a ball is removed, 10 balls have been added, and 9/10 > >> of the balls inserted remain. Therefore, at no time before noon is the > >> vase empty. Agreed? > >> > >> Events including insertions and removals only occur at times t of the > >> form t=-1/n, where n e N. Where noon means t=0, there is no t such that > >> -1/n=0. Therefore, no insertions or removals can occur at noon. Agreed? > >> > >> Balls can only leave the vase by removal, each of which must occur at > >> some t=-1/n. The vase can only become empty if balls leave. Therefore > >> the vase cannot become empty at noon. Agreed? > > > > Not so fast. What do "become empty" or "become empty at" mean? > > > > "Not so fast"???? We've been laboring this point endlessly. The vase > goes from a state of balledness to a state of balllessness starting at > time 0. Balls have to have been removed for this transition to occur. And have been.
From: Virgil on 25 Oct 2006 16:11 In article <453fb693(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > Virgil wrote: > >> In article <453e824b(a)news2.lightlink.com>, > >> Tony Orlow <tony(a)lightlink.com> wrote: > >>> Virgil wrote: > >>>> In article <453e4a85(a)news2.lightlink.com>, > >>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>> If the vase exists at noon, then it has an uncountable number of balls > >>>>> labeled with infinite values. But, no infinite values are allowed i the > >>>>> experiment, so this cannot happen, and noon is excluded. > >>>> So did the North Koreans nuke the vase before noon? > >>>> > >>>> The only relevant issue is whether according to the rules set up in the > >>>> problem, is each ball inserted before noon also removed before noon?" > >>>> > >>>> An affirmative confirms that the vase is empty at noon. > >>>> A negative directly violates the conditions of the problem. > >>>> > >>>> How does TO answer? > >>> You can repeat the same inane nonsense 25 more times, if you want. I > >>> already answered the question. It's not my problem that you can't > >>> understand it. > >> It is a good deal less inane and less nonsensical than trying to > >> maintain, as TO and his ilk do, that a vase from which every ball has > >> been removed before noon contains any balls at noon that have not been > >> removed. > > > > Ah, you are forgetting the balls labeled with "infinite values". Those > > balls haven't been removed before noon. Although, I must say I'm not too > > clear on when they were added. > > > > At noon Where in the original problem does it say anything like that?
From: Virgil on 25 Oct 2006 16:14 In article <453fb773$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > So, there is no problem in deriving a contradiction from your set of > assumptions? I thought that's all you cared about. There is no contradiction in the standard reading, however confused TO may be about it. > > > > > Tony has a strange problem with this, causing him to write mangled > > versions of Om mani padme hum, and protest that this is a "Greatest > > natural objection". For some reason he seems to accept that there is no > > greatest natural number, yet feels that appealing to this fact in an > > argument is somehow unfair. > > > > > > I goes like this: > > > "No Largest Finite!!!! (GONG!!!) Huyah huyah huyah.....Ommmmmmmmega!" TO goes like that continually, to the detriment of his ability to produce logical thought/
From: Virgil on 25 Oct 2006 16:15 In article <453fb796(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <1161754218.785144.91070(a)e3g2000cwe.googlegroups.com>, > > imaginatorium(a)despammed.com wrote: > > > >> David Marcus wrote: > >>> Tony Orlow wrote: > >>>> David Marcus wrote: > >>>>> Tony Orlow wrote: > >>>>>> As each ball n is removed, how many remain? > >>>>> 9n. > >>>>> > >>>>>> Can any be removed and leave an empty vase? > >>>>> Not sure what you are asking. > >>>> If, for all n e N, n>0, the number of balls remaining after n's removal > >>>> is 9n, does there exist any n e N which, after its removal, leaves 0? > >>> I don't know what you mean by "after its removal"? > >> Oh, I think this is clear, actually. Tony means: is there a ball (call > >> it ball P) such that after the removal of ball P, zero balls remain. > >> > >> The answer is "No", obviously. If there were, it would be a > >> contradiction (following the stated rules of the experiment for the > >> moment) with the fact that ball P must have a pofnat p written on it, > >> and the pofnat 10p (or similar) must be inserted at the moment ball P > >> is removed. > >> > >> Now to you and me, this is all obvious, and no "problem" whatsoever, > >> because if ball P existed it would have to be the "last natural > >> number", and there is no last natural number. > >> > >> Tony has a strange problem with this, causing him to write mangled > >> versions of Om mani padme hum, and protest that this is a "Greatest > >> natural objection". For some reason he seems to accept that there is no > >> greatest natural number, yet feels that appealing to this fact in an > >> argument is somehow unfair. > >> > >> > >>>> Sure. But it's easily explainable and resolvable once a proper measure > >>>> is applied to the situation. Omega doesn't lend itself to proper > >>>> measure. Infinite series do. Bijection loses measure for infinite sets. > >>>> N=S^L and IFR preserve measure. > >> Oh, right, well Tony has a number of "explanations" for things, most of > >> them equally mysterious. > >> > >> Brian Chandler > >> http://imaginatorium.org > > > > And many of them downright wrong! > > WRONG!!!! YES, WRONG!!!!
From: MoeBlee on 25 Oct 2006 16:20
Tony Orlow wrote: > > But none of Robinson's non-standard numbers are cardinalities. > > No kidding. They actually make sense. You said you have not properly studied chapter II in the book - the one that includes mathematical logic, model theory, and set theory (does it not? I'll stand corrected if it doesn't). What are you going to say when you find out that what you say makes sense rests on a foundation of set theory that you say doesn't make sense? Or, if I'm incorrect that Robinson's work in non-standard analysis doesn't presuppose basic mathematical logic, model theory, and set theory, then I'll benefit by being corrected in my admittedly cursory understanding of the matter. MoeBlee |